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2061quiz01bs

# 2061quiz01bs - MATHZOGl LINEAR MATHEMATICS QUIZ VERSION 13...

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Unformatted text preview: MATHZOGl LINEAR MATHEMATICS QUIZ VERSION 13 Name: WW... SID: This quiz paper consists of three sheets of paper. There are ﬁve questions worth a total of 45 marks—~marks available for each part are indicated. The quiz runs for 45 minutes. Write your answers and working in the blank spaces provided. The last page is left blank for rough working which will not be marked. S:{(;).R2 m}. (a) Show that S is dosed under addition. [5 marks] Le+ X:[C]Iug:[:l]e§, Then aka—£920 anal CWC‘RZO. 1. Let New X+KQ :: O‘AD‘ Cm+C3a~G>+00 :2 (A*£>+(c~ol>>/O +0 :1 0 so V+wes m T1415, gal/\OVOS g 15: C5984 under“ oxoloh‘kovx. (b) Show that S is not closed under scalar multipiication. [4 marks] [Hes space {30 bM-‘r («~0[é]ﬁ[ﬁg]¢g s‘mce “(<0 The, skews 9 15 W64” CIOSeoi MHAEV QCaloxw!“ MMWIH] awoL'L‘t om, 2. (a) Find the cartesian equation of the plane Span(X) for the set x={<§>=(~:6>,<;>}« {2166M (>0 «5% {3}“[MHHEJ {\Ox {iobc [(036 o-éZ 30K 3 N O “Q 2 j A“ O“6 Z 5 T—(IL'Q. QUGJ’QW‘ COWQKS‘Pe’A-lr i"g'DC”-% U ".10 go QFQM(X>:§[Z]E’R3 QXL—«F «~2azo (b) Show that the subset {f, g, h} of ]F is lineariy indepenéent where ﬂan) = 1, g(\$) = :c m 5, z: 3:2 + 3x — 10. [4 marks] Le} 0k ( O +£bc~€> +c(vc,1+3.>c.~lo)-.;O, new (“‘93 “(063+ (lyi—Bcbzc fiat:t : C) so IO~SL>~IOcnO b+?>lc “KO C :0 grit/\C-ﬁ r {{{DQIDC'l-i "g hmﬁod’LLr “InAePequ+ mere-Coﬂkﬁ okz£zct0 VOLGCLI eke bog 1% KRVLeaHj ‘lﬂA€i>€.\/\A€,J\+, 3. Let 93 V={(y) €333 5mwy=82}. Z (a) Finé a basis {11,V} of V. {6 marks} {31> gxuj=8%<—=:) ngxwgi @% x x. g % [g]=[9:—8z]wx{g]+%[l] O 90 E:{[l5:l2{}3]g éI-paws O E g 19 “wearlj TnAePemolw+ SFKCQ.“€;‘H\U \lechoJ‘ “m E 7% a scalar MMHNFLQ 0? HM? oJrLef. Mamba E “‘62 Du [341619 0-? (b) Find a vector W in R3 which is not in V. [2 marks] bar—:[éjetv game gamma» 0 (0) Explain why {11, V, W} is a. basis of R3. [3 marks] ilk \l W “.9 hmamvkj nut/x. mva QévrgFam(g,g). W42. oJeo leu/Q chum (WU-LE. so {£194,933 \5 a £704,365 0’? i“ V 3% linearly lchlQF'emAQAA‘X” 4. Let p be the unique polynomial in 3% that ﬁts the following (late. In In (a) Write down the Lagrange basis {103,191,302} for the data. [6 marks] (b) Use the Lagrange basis to ﬁnd a, formula for p. [2 marks] lobe): lZFo (xB—E 2F! (2:) +OF2(>C> 2: Z(:ac‘-2>(°C‘33 “>C(¢>C “3) .2: 2(x1~f;x +6) -- (ac:2 rgac) 213112 “:l‘bc +l2 ((3) Estimate the value of y when :1: m 1. [2 marks] t)me nil—1H0 +12 :6 5. Let 125 1432514. 347 f (a) Find the reduced row echelon form J 0 A. [2 marks] E25 ‘25 ‘03 A12§3M‘~O \% N 0"+:3 an; “2‘3 000 Etﬁpz‘ZP‘ R‘QRFZRI R5“? PS’SR‘ R335 P232121 (b) Find a basis of the column space of A. {2 marks] The {Ewe-L “Ludo cohww/xe 0-? T are 0“ lows of; com) 670 He 9%ng Leo Comm 0.? A Our-«e Ox 3290\6‘15 010 Cowﬂuie :5 a (page, 010 COM/4). (c) Find a. basis of the null space of A. {2 marks] #7 m Q Ma. LEJF %7‘~‘E. WM dzwklr-E’ 3C23'h mmol W 90 {u} °*‘ (d) Verify that the sum of the rank and she nuliity of A is equai to ihe number of coiumns of A. [1 mark] bam\L(/1Q + Wu\\‘1‘l-j: Z2+l13_ ...
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2061quiz01bs - MATHZOGl LINEAR MATHEMATICS QUIZ VERSION 13...

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